Boyd Cordner and Milne were both taken off for head injury assessments in the wake of a head clash in the tackle; the Dragons subsequently getting a penalty instead of the Roosters benefiting from a knock-on.
"We lost the game, we lost it in the first half. It wasn't good enough from us," Robinson said.
"But I am not going to sit here and allow poor decisions to go by just because of a rule and I am not going to allow referees not to talk in the way that they should to our players over years and I feel strongly enough about it.".
"The bunker decides they are going to play the match review committee and call a penalty.
"The bunker has decided to be the onfield referee today, they jumped in at every occasion, they are not the match review committee.
"It was just soft on Anzac Day. We want to play a tough game and they were soft calls coming from the bunker, they were not good enough."
Robinson said his side were denied a fair chance to win the game because of the call against Napa.
He said Cummins had ongoing issues with the Roosters.
"Ben has been horrible and disrespectful to our players for many years and it has continued," Robinson said.
"We have had a good high percentage win rate until this year ... he speaks poorly to our players. He won't look them in the eye.
"The way that he spoke to (captain) Jake (Friend) during the game was unacceptable."
The Roosters have won just seven of 36 penalty counts under Cummins.
Friend said Cummins refused to talk to him about refereeing decisions.
Roosters chairman Nick Politis and John Lee were present at the post-game press conference as Robinson made the comments that put him at risk of a $10,000 fine under rules preventing NRL coaches from criticising the performance of referees.
It is a situation Robinson realises he is in.
"I would say (NRL CEO) Todd (Greenberg) might be ringing me," he said.
In other games in round eight, Brisbane beat South Sydney 30-8 at Suncorp Stadium on Friday night.
Canterbury downed Gold Coast 21-20 in golden point at ANZ Stadium on Saturday.
Canberra thrashed Wests Tigers 60-6 in the nation's capital on Saturday evening.
North Queensland kept their impressive home record intact with a 32-16 win over Parramatta on Saturday night.
Cronulla defeated Penrith 20-18 at Shark Park on Sunday while Manly were too good for Newcastle, 26-10, at Hunter Stadium on Monday.
In the round's final fixture Melbourne thrashed the Warriors 42-0 at AAMI Park.